comparison of ordinary kriging, regression kriging, and cokriging techniques to estimate soil...

Comparison of Ordinary Kriging, Regression Kriging,and Cokriging Techniques to Estimate Soil Salinity

Using LANDSAT ImagesAhmed A. Eldeiry1 and Luis A. Garcia2

Abstract: The objectives of this study are: �1� to evaluate the LANDSAT best band combinations to estimate soil salinity with differentcrop types; �2� to compare ordinary kriging, regression kriging, and cokriging techniques to generate accurate soil salinity maps whenapplied to LANDSAT images; and �3� to compare the performance of different crop types: alfalfa, cantaloupe, corn, and wheat asindicators of soil salinity. This study was conducted in an area in the southern part of the Arkansas River Basin in Colorado. SixLANDSAT images acquired during the years: 2000, 2001, 2003, 2004, 2005, and 2006 in conjunction with field data were used to estimatesoil salinity in the study area. The optimal subsets of band combinations from the LANDSAT images that correlate best with the soilsalinity data sets were selected. Ordinary kriging, regression kriging, and cokriging were applied to 2,914 soil salinity data points collectedin alfalfa, cantaloupe, corn, and wheat fields in conjunction with the selected LANDSAT image band combination subsets. Ordinaryleast-squares �OLSs� were used to regress the correlated band combinations to generate a soil salinity surface. The residuals of the OLSmultiple regression model were kriged and combined with the soil salinity surface generated using the OLS multiple regression model toproduce the final soil salinity surface of the regression kriging model. The same LANDSAT band combinations used with the regressionkriging technique were used as secondary data variables with the cokriging technique, while the soil salinity data was used as a primaryvariable. The results show that the best band combinations for estimating soil salinity with different crops are as follows: alfalfa �red, nearinfrared, and normalized difference vegetation index �NDVI��; cantaloupe �blue and green�; corn �near, thermal, and NDVI�; and wheat�blue and thermal�. The performance of the different geostatistical models used in this study is: �1� ordinary kriging; �2� regressionkriging; and �3� cokriging. Estimation of soil salinity works best for corn, then wheat, cantaloupe, and alfalfa.

DOI: 10.1061/�ASCE�IR.1943-4774.0000208

CE Database subject headings: Soil properties; Salinity; Remote sensing; Agriculture; Crops.

Author keywords: Ordinary kriging; Cokriging; Regression kriging; Soil salinity; Remote sensing; LANDSAT; Alfalfa; Corn; Wheat;Cantaloupe.

Introduction

Geostatistics is a branch of statistical theory concerned with prob-lems of spatial serial data, interpolation and mapping of distrib-uted data, and related problems. Generally, the methods used arethose of time series analysis, adapted and extended to spatial data�Ripley 1981�. Spatial autocorrelation is problematic for classicalstatistical tests, such as ANOVA and ordinary least-squares�OLSs� regression which assume independently distributed errors�Haining 1990; Legendre 1993�. When there is autocorrelation,the assumption of independence is often invalid, and the effects ofcovariates that are themselves autocorrelated tend to be exagger-ated �Gumpertz et al. 1997�. A spatial pattern in the residuals from

1Ph.D. Research Fellow, Dept. of Civil and Environmental Engi-neering, Integrated Decision Support Group, Colorado State Univ.,CO 80523. E-mail: aeldeiry@rams.colostate.edu

2Director and Professor, Department of Civil and EnvironmentalEngineering, Integrated Decision Support Group, Colorado State Univ.,CO 80523 �corresponding author�. E-mail: Luis.Garcia@Colostate.edu

Note. This manuscript was submitted on February 23, 2009; approvedon December 10, 2009; published online on May 14, 2010. Discussionperiod open until November 1, 2010; separate discussions must be sub-mitted for individual papers. This paper is part of the Journal of Irriga-tion and Drainage Engineering, Vol. 136, No. 6, June 1, 2010. ©ASCE,

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the OLS models may result from failure to include or adequatelymeasure autocorrelation �Lichstein et al. 2002�. Kriging modelsestimate the values at unsampled locations by a weighted averag-ing of nearby samples. The correlations among neighboring val-ues are modeled as a function of the geographic distance betweenthe points across the study area, defined by a variogram �Milleret al. 2007�. Although kriging provides a mechanism for combin-ing global and local information in predictions, the ability of thevariogram to describe spatial dependence is directly a function ofthe quantity and quality of the sample data �Miller et al. 2007�.

The spatial structure of the residuals from the multiple regres-sion models is usually analyzed using a geostatistical method, thevariogram, which has been widely used to analyze spatial struc-tures in ecology �Phillips 1986; Robertson 1987�. The empiricalvariogram, which is a plot of the values of ��h� as a function ofh, gives information on the spatial dependency of the variable.Triantafilis et al. �2001� used geostatistical methods such as ordi-nary kriging �OK�, regression kriging �RK�, three-dimensionalkriging, and cokriging �CK�. These methods were tested with araw electromagnetic induction instrument �EM-38� in a soil elec-trical conductivity survey. They compared their methods, on thebasis of precision and bias in soil salinity estimates, and foundthat RK performed the best. Eldeiry and Garcia �2008a� comparedthree statistical models �OLS, spatial autoregressive, and a modi-

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sensing. Their results show that the spatial pattern in the residualsfrom the OLS multiple regression models always involve autocor-relation, and when those residuals are kriged and combined withthe OLS multiple regression surface to produce the modified re-sidual kriging model, it provides the best results. Eldeiry et al.�2008� evaluated the use of a modified residual kriging model toreduce the number of soil salinity samples that need to be col-lected in alfalfa fields. They found that when using modified re-sidual kriging, the number of soil samples that need to becollected can be reduced significantly without impacting the ac-curacy of the results.

RK involves various combinations of linear regressions andkriging. The simplest model is based on a normal regression fol-lowed by OK with the regression residuals �Odeh et al. 1995�. CKtakes advantage of the correlation that may exist between thevariable of interest and other more easily measured variables�Odeh et al. 1995�. CK is the most versatile and rigorous statisti-cal technique for spatial point estimation when both primary andsecondary �covariate� attributes are available and has been usedwidely in soil science �Vauclin et al. 1983; Trangmar et al. 1987;Yates and Warrick 1987�.

Howari �2003� used supervised classification, spectral ex-traction, and matching techniques to investigate the types andoccurrences of salt in the Rio Grande valley in the United States-Mexico border. He established the soil groups using soil physio-chemical properties and image elements �absorption-reflectivityprofiles, band combinations, gray tones of the investigated im-ages, and textures of soil and vegetation covers as they appear inthe images�. Eldeiry and Garcia �2008b� compared the perfor-mance of different satellite images �IKONOS, LANDSAT, andASTER� for estimating soil salinity in alfalfa and corn fields.They found that the IKONOS images performed the best in esti-mating soil salinity in both alfalfa and corn fields, while cornfields performed better than alfalfa fields. Aerial photography,videography, infrared thermometry, and multispectral scannershave also been used to detect, map, and monitor salt affected soils�Robbins and Wiegand 1990�; sources of multispectral imagesthat have been found useful include LANDSAT, SPOT, and theIndian Remote Sensing series of satellites �Dwivedi and Rao1992�. Fernández-Buces et al. �2006� correlated soil salinity char-acteristics with the spectral response of plant species and baresoils. They calculated a Combined Spectral Response Index forbare soils and vegetation by adjusting the normalized differencevegetation index �NDVI�. Farifteh et al. �2006� mentioned thatmost salinity studies have focused on severely saline areas andhave given less attention to the detection and monitoring ofslightly or moderately affected areas. They determined that amajor constraint was the nature of the satellite images, which donot allow for extracting information from the third dimension ofthe soil body, e.g., where salts concentrate in the subsoil. There-fore, they used a transport model to predict the salt distribution inthe subsoil.

The lower Arkansas River Basin of Colorado has been con-tinuously irrigated since the 1870s and began to develop highsaline water tables by the early part of the twentieth century�Miles 1977�. Currently, the Arkansas River is one of the mostsaline rivers in the United States �Tanji 1990; Miles 1977�. Saltsdecrease the availability of water to plants due to increase os-motic potential, and have a direct adverse effect on the plantmetabolism �Douaik et al. 2003; Greenway and Munns 1980�.Crop yield reduction in fields in the Lower Arkansas Valley due tosalinization has been estimated to be 0–75% with a total revenue

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et al. 2002�. Many factors could affect the crop vegetation appear-ance such as: soil characteristics, irrigation schemes, weather con-ditions, diseases, pests, and crop management. Some areas mightbe affected heavily by one or more factors rather than the othersdepending on the conditions and agricultural practices of thatarea. However, many of these factors are temporary and thereforeonly affect either crops for a portion of an irrigation season or partof a field. However, the impacts of soil salinity on a particularcrop are more consistent over time and in areas with severe prob-lems the impacts are wide spread.

Many studies �Stein et al. 1988; Stein and Corsten 1991;Zhang et al. 1992, 1997; Istok et al. 1993� have shown the supe-riority of CK to OK in mapping soil salinity. However, others�Shouse et al. 1990; Martinez-Cob 1996� have shown that CKwas only minimally superior to OK when auxiliary variables werenot highly correlated to the primary variables. In this study thegeostatistical approach was used with LANDSAT images to esti-mate soil salinity using different crops as indicators of soil salin-ity. This study focuses on the autocorrelation among the soilsalinity data and the cross correlation between soil salinity dataand the correlated LANDSAT bands. The higher the autocorrela-tion among soil salinity data, the more likely that OK will per-form better in mapping soil salinity. The higher the crosscorrelation between soil salinity data and the correlated bands ofthe LANDSAT images, the more likely that either RK or CK willperform better in mapping soil salinity. This study also focuses onusing different crops as indicators since each crop appearance isdifferent from another which produces a different spectral reflec-tion when the image is acquired. Bare soil was not used for thisstudy since it is hard to find bare soil without weeds or vegetationor covered with snow in the study area.

The possible restriction for this methodology is that it is hardto apply where the parcel sizes are very small, such as in somecountries where the parcel sizes are less than one-fourth of ahectare, and each parcel can be planted with a different crop. It islikely that a tall or dense crop can be planted next to a small andsparse crop in the neighboring parcel which can give a false in-dication on the effect of soil salinity when using the spectralreflection of remote sensing data given the size of the LANDSATimage pixels.

Materials and Methods

Site Description

This research was conducted as part of a project that ColoradoState University is conducting in the Arkansas River Basin insouthern Colorado �Fig. 1�. Crops in this area include alfalfa,corn, wheat, onions, cantaloupe, and other vegetables. Thesecrops are irrigated by a variety of irrigation systems includingborder and basin, furrow, center pivots, and a few subsurface drip.Salinity levels in the irrigation canals along the river increasefrom 300 ppm total dissolved solids near Pueblo to over 4,000ppm at the Colorado-Kansas border �Gates et al. 2002, 2006�.This study focused on fields cultivated with alfalfa, cantaloupe,corn, and wheat, since soil salinity data was collected in fieldswhere these crops were being grown. Soil salinity was measuredin these fields using an electromagnetic induction instrument�EM-38�.

Table 1 shows the description of the data used in this study.The total number of soil salinity points is 2,914 distributed among

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study represent different ranges of soil salinity from low, moder-ate, to high. Soil salinity data was based on data collected usingan EM-38 electromagnetic probe and calibrated using soilsamples that were analyzed using a Hach salinity kit �Eldeiry andGarcia 2008a�.

Satellite Images and Image Processing

Six LANDSAT images acquired during July 12, 2000 �LAND-SAT 7�; July 8, 2001 �LANDSAT 7�; July 22, 2003 �LANDSAT5�; August 9, 2004 �LANDSAT 5�; July 27, 2005 �LANDSAT 5�;and July 30, 2006 �LANDSAT 5� were used in this study. Theswitch from LANDSAT 7 to LANDSAT 5 is due to the failure ofthe scan line corrector �SLC� in the ETM+ on May 31, 2003. Theeffect is that approximately one-fourth of the data in a LANDSAT7 scene is missing when acquired without a functioning SLC.These images were evaluated to assess soil salinity with differentcrop types. Spatial distortion of the images was corrected using ageometric correction model in ERDAS Imagine 8.7 �ERDASImagine 2006�, so that the points on the image match with thesame points on the ground. A dark object correction was used tocompensate for the effect of atmospheric scattering �Song et al.2001�. The NDVI was added as an additional band to each image.The NDVI uses the contrast between red and infrared reflectanceas an indicator of vegetation cover and vigor. The LANDSAT 5images contained three visible bands �blue, green, and red�, twonear infrared bands, one thermal band; and a mid-IR band.LANDSAT 7 images contained three visible bands �blue, green,and red�, one near infrared band, two shortwave infrared bands�MIR-1 and MIR-2�, a thermal infrared band, and a panchromaticband.

Table 1. Description of Soil Salinity Data Points Collected in the StudyArea

Crop YearSoil salinitydata points

Soil salinity range�dS/m�

Alfalfa 2004, 2005, 2006 989 1.16–32.34

Cantaloupe 2004, 2005, 2006 1,102 1.35–14.27

Corn 2000, 2001 518 1.43–19.50

Wheat 2003, 2005 305 1.48–31.26

Fig. 1. Study area in the Arkansas River Basin in southern Colorado

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Correlated Band Combinations

Stepwise regression was used to select the band combination thathad the best correlation with the observed soil salinity data whileminimizing the Akakie information corrected criteria �AICC��Akaike 1977; Brockwell and Davis 1991�. Among the differentbands of each image, the stepwise regression technique assignstrue �T� to each band that is correlated with soil salinity and false�F� to each band that is not correlated. In addition to the stepwiseregression, the optimal model function in the S+ statistical soft-ware package was used to select the best set of bands when usingone, two, three, and up to all bands. Out of these selected sets ofbands, the optimal model function selects the band combinationwith the smallest AICC value as the optimal set. The stepwiseregression is based on whether the band is correlated to soil sa-linity �T� or not �F�, while the optimal model function evaluatesthe sets of bands based on the smallest AICC value. However,none of these models include the p-value of the selected bandswhich should be checked to guarantee that the selected bandshave a significant cross correlation with the soil salinity data.Therefore, when applying the OLS multiple regression model tothe selected bands, the p-value was checked and if the p-value ofany band exceeded 0.05, this band was removed.

OK Technique

The OK model estimates the values at unsampled locations by aweighted averaging of nearby samples. The correlations amongneighboring values are modeled as a function of the geographicdistance between the points across the study area, defined by avariogram �Miller et al. 2007�. The spatial distribution of the soilsalinity data was analyzed using the variogram, which has beenwidely used to analyze spatial structures in ecology �Phillips1986; Robertson 1987�. The sample variogram, ��h� is estimatedby the following equation:

��h� =1

2N�h� �i=1

N�h�

��si� − ��si + h��2 �1�

where ��si� and ��si+h�=estimated residuals from the multipleregression models at locations si and si+h, a location separated bydistance h and N�h�=total number of pairs of samples separatedby distance h. The empirical variogram, which is a plot of thevalues of ��h� as a function of h, gives information on the spatialdependency of the variable. Exponential, Gaussian and Sphericalmodels were fitted to the sample variograms using a weightedleast-squares method �Robertson 1987�. The variogram modelwith the smallest AICC was selected to describe the spatial de-pendencies in the soil salinity data. In all three models the samenumber of neighbors, resolution, and variogram were used toavoid introducing bias into the results.

RK Technique

RK involves spatially interpolating the residuals from a nonspa-tial model �e.g., OLS� using kriging, and adding the results to theprediction obtained from the nonspatial model �Goovaerts 1997�.Stepwise and the optimal model procedures were used to identifythe best subset of satellite bands to include in the regression mod-els that minimized the AICC �Akaike 1977; Brockwell and Davis1991�. OLS was used to regress the soil salinity data using thevalues of the corresponding satellite bands and the NDVI index.

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�Eldeiry and Garcia 2008a� to produce the final surface of the RKtechnique. The RK technique modeling process was accom-plished as follows:

The variability in the soil salinity as a function of the satelliteimage bands was explored by multiple regression analysis usingthe following equation:

z�so� = �0 + �1x1�so� + . . . + �kxk�so� �2�

where z�so�=estimated soil salinity at spatial location, s0; �i

=estimated regression coefficients; and xi=independent variables�satellite bands� at spatial location, s0.

The residuals of the OLS model were checked for correlation.If they were spatially correlated, OK was used to model the spa-tial distribution of soil salinity in the fields. At every locationwhere there are no samples, estimates of the true unknown residu-als, ��so�, were obtained using a weighted linear combination ofthe available samples at spatial locations, si as follows:

��so� = �i=1

wi��si� �3�

where the set of weights, wj, takes into consideration the dis-tances between sample locations and spatial continuity, or clus-tering between the samples. The best fitting variogram model thathad the smallest AICC value was used to describe the spatialcontinuity in estimating the kriging weights.

CK Technique

CK equations for estimating a primary variable from a set ofvariables are extensions of those for kriging. CK works bestwhere the primary variable of interest is less densely sampledthan the others. Soil salinity is the primary variable and the othervariable�s� represent the pixels of the LANDSAT band combina-tions. The same band combination that was used with the RK wasused as secondary variables with the CK technique while soilsalinity measurements were used as a primary variable.

The predicted soil salinity using CK can be written as �Li andYeh 1999�

f0� = �

n ��0i f i + �j=1

�0i,jhi,j� �4�

where n=number of soil salinity data points; f0�=predicted value

of soil salinity, at location xo; f i=value of soil salinity; �0i=CKweights of the soil salinity; m=number of cross correlated bands;�0i,j =CK weights of the cross correlated band j at location i; andhi,j =pixel values of each cross correlated band j at location i.

More details on OK, RK, and corkriging equations can befound on Journel and Huijbregts �1978�; Vauclin et al. �1983�;Yates and Warrick �1987�; Isaaks and Srivastava �1989�.

Using LANDSAT Images with RK Model

The process for using LANDSAT images with the RK model foralfalfa, cantaloupe, corn, and wheat are the following:• Each LANDSAT image was geometrically corrected and then

converted into its individual bands in the forms of grids;• Each data set of soil salinity was combined with the spectral

properties of the field samples though the overlay of samplinglocations with individual satellite bands using a geographic

• X ,Y-coordinates of the sample locations were used to extractthe pixel values for each of the bands;

• A matrix was constructed where the first two columns repre-sent the X- and Y-coordinates, the third column represents thesoil salinity sample values, and the rest of the columns repre-sent the different bands pixel values. The rows of the matrixrepresent the number of samples points;

• A forward stepwise regression procedure in the S+ statisticalsoftware package was used to identify the best subset ofLANDSAT bands from the previous matrix to include in theregression models that minimize the AICC values. In additionto the stepwise regression, the optimal model function in S+was used to select the best band combinations that have crosscorrelation with the soil salinity data;

• Only the correlated bands are kept while the non correlatedbands are removed from the matrix;

• OLS was used to explore the variability in soil salinity as afunction of the LANDSAT image bands using the followingequation:

z�so� = �0 + �1x1�so� + . . . + �kxk�so� �5�

where z�so�=predicted soil salinity at spatial location, so; �i

=estimated regression coefficients; and xi=independent vari-ables �i.e., LANDSAT bands� at spatial location, so;

• To guarantee a strong cross correlation between soil salinitydata and the correlated bands, p-values should be less than0.05. If any band shows a p-value of less than 0.05, this bandis removed;

• A surface is generated for the OLS multiple regression modelfrom the correlated bands of LANDSAT image;

• Another surface is generated for the residuals using an OKtechnique; and

• A RK surface was generated by combining the surface gener-ated using the OLS multiple regression model and the othersurface generated from the kriged residuals.

Using LANDSAT Images with CK Kriging Model

The same bands that proved to have high cross correlation withthe soil salinity data were used with the CK model as secondaryor auxiliary variables, while the soil salinity data was used as theprimary variable. With the CK model there is no need to run anyregression among the variables. When generating a CK surfaceeither in ArcGIS or S+, soil salinity data are used as the primaryvariable and the cross correlated bands are used as auxiliary vari-ables. For each soil salinity data set with each crop, the correlatedbands are different from one set to another depending on the crosscorrelation among the soil salinity data and the LANDSAT imagebands. The same number of neighbors, cell size �resolution�, andvariogram models was used with both the RK and the CK modelsto avoid introducing bias into the results.

Model Calibration and Validation

A total number of 2,914 soil salinity data points were used for thecalibration and validation of the different models. These pointswere distributed among different crops as shown in Table 3. Datasets were selected from a range of years spanning from 2000 to2006 where each crop had been planted for at least two years toallow the use of one year of data for calibration and another yearof data for validation. Alfalfa data sets were collected in 2004,

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sets for 2004 and 2006 with a total number of 534 points wereused for the calibration process while the data set for 2005 with atotal number of 455 points was used for the validation processes.The cantaloupe data sets were collected in 2004, 2005, and 2006with a total number 1,102 points. Data sets for 2004 and 2005with a total number of 875 points were used for the calibrationprocess while the data set for 2006 with a total number of 227points was used for the validation processes. The corn data setswere collected in 2000 and 2001 with a total number of 518points. The data set for 2001 with a total number of 325 pointswas used for the calibration process while the data set for 2000with a total number of 193 points was used for the validationprocesses. The wheat data sets were collected in 2003 and 2005with a total number of 305 points. The data set for 2005 with atotal number of 238 points was used for the calibration processwhile the data set for 2003 with a total number of 67 points wasused for the validation processes.

Model Evaluation

The evaluation of the models is based on the following param-eters:• The accuracy was evaluated by the normalized mean-absolute

error �NMAE� �Journel 1984� and the normalized root-mean-square error �NRMSE�. The NMAE was defined as follows:

NMAE = 100%

�i=1

�zi − zi�

�i=1

�6�

The NRMSE was calculated as follows:

NRMSE = 100%

�i=1

�zi − zi�2

M �i=1

�7�

where zi=estimate of soil salinity z at location i; zi=true valueof soil salinity z at location i; and i=1,2 , . . . . . . . ,M.Both the NMAE and NRMSE are measures of the global av-

erage deviation between the estimated values and the true values.The NRMSE is the most commonly used criterion, although theNMAE was mentioned to be more robust than the NRMSE �Jour-nel 1984�.• The effectiveness was evaluated using a goodness-of-

prediction statistic �G� �Agterberg 1984; Kravchenko and

Table 2. Selected Bands Combinations for Alfalfa, Cantaloupe, Corn,and Wheat

Crop Selected bands �spectral resolution�

Alfalfa Red �0.63–0.69 �m�, near infrared �0.76–0.90 �m�,and NDVI �0.63–0.9 �m�

Cantaloupe Blue �0.45–0.52 �m� and green �0.51–0.60 �m�Corn Near infrared �0.76–0.90 �m�, thermal �8–12 �m�,

and NDVI �0.63–0.9 �m�Wheat Blue �0.45–0.52 �m� and thermal �8–12 �m�

Bullock 1999; Guisan and Zimmermann 2000; Schloeder et al.

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2001�. The G-value measures how effective a prediction mightbe relative to that which could have been derived by using thesample mean �Agterberg 1984�

G = �1 −��i=1

�Zi − Zi�2/�i=1

�Zi − Z�2� �8�

where Zi=observed value of the ith observation of soil salin-

ity; Zi=estimated value of the ith observation of soil salinity;

and Z=soil salinity sample mean. A G-value equal to 1 indi-cates perfect prediction, a positive value indicates a more re-liable model than if the sample mean had been used, anegative value indicates a less reliable model than if thesample mean had been used, and a value of zero indicates thatthe sample mean should be used.

Results

Table 2 shows the selected bands for alfalfa, cantaloupe, corn, andwheat. The best band combinations were selected based on thecriteria that the p-value of each band be less than 0.05 while theAICC value of the selected band combination be the smallest. Theselected band combinations for each crop were: alfalfa: red, nearinfrared, and NDVI with spectral resolutions of �0.63–0.69 �m�,�0.76–0.90 �m�, and �0.63–0.9 �m�, respectively; cantaloupe:blue and green with spectral resolutions of �0.45–0.52 �m� and�0.51–0.60 �m�, respectively; corn: near infrared, thermal, andNDVI with spectral resolutions of �0.76–0.90 �m�, �8–12 �m�,and �0.63–0.9 �m�, respectively; and wheat: blue and thermalwith spectral resolutions of �0.45–0.52 �m� and �8–12 �m�,respectively.

Fig. 2 shows the scatter plots of estimated versus observed soilsalinity data for alfalfa, cantaloupe, corn, and wheat fields usingthe OK, RK, and CK models. Scatter plots are one of the basictools of quality control and are especially useful when there arelarge numbers of data points as in the case of this study �2,914pints�. They provide information about the relationship betweentwo variables for the: �1� strength; �2� shape �linear, nonlinear,etc�; �3� direction—positive or negative; and �4� presence of out-liers. The strength of the relationship between the observed andpredicted soil salinity data are the strongest with wheat, then corn,cantaloupe, and alfalfa. OK performed the best among the othermodels regarding the strength of the relationship. Observed andestimated soil salinity relationships are closer to a linear relation-ship for cantaloupe, corn, and wheat while this relationship iscloser to nonlinear for alfalfa. All the relationships between theobserved and estimated soil salinity data using all the models arepositive since the trend is rising. The scatter plots for all the cropsand models tend to have some outliers at different levels.

Fig. 3 shows the histogram plots of the observed and estimateddata for alfalfa, cantaloupe, corn, and wheat when using the OK,RK, and CK models. Histograms can provide information about:

Table 3. Number of Points Used for the Calibration and ValidationProcesses

Alfalfa Cantaloupe Corn Wheat

Calibration 534�2004, 2006�

875�2004, 2005�

325 �2001� 238 �2005�

Validation 455 �2005� 227 �2006� 193 �2000� 67 �2003�

�1� the mode, the value that occurred most frequently; �2� an

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Fig. 2. Scatter plots of estimated versus observed soil salinity for alfalfa, cantaloupe, corn, and wheat fields using OK, RK, and CK models

Fig. 3. Histogram plots of the observed data and the data produced by OK, RK, and CK models for alfalfa, cantaloupe, corn, and wheat

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indication of the overall variation, by comparing the smallest andlargest value; and �3� the shape of the distribution, normal, orskewed. The mode values of alfalfa, cantaloupe, corn, and wheatfor the observed data are between 1 and 3 dS/m. OK, RK, and CKmodels were successful in maintaining the mode values for allcrops. The mode frequency is the highest for wheat followed bycantaloupe and moderate for alfalfa and corn. The three modelswere successful in maintaining the frequency for most crops ex-cept for alfalfa where it was underestimated. The overall variationis largest in wheat and smallest in cantaloupe while moderate inalfalfa and corn. The three models were successful in maintainingthe overall variation for most crops except OK with alfalfa. Thedistributions of all crops for the observed and estimated datausing the three models follow the right-skewed distribution wherethe peak is off the center toward the limit and a tail stretches awayto the right. The skewness is highest in wheat and smallest incantaloupe and moderate in alfalfa and corn. Both the scatter plotsand histograms are quality control tools and in order to quantita-tively summarize the data a set of box-and-whisker plots has beendeveloped.

Figs. 4�a and b� show the box-and-whiskers plots of the ob-served and estimated data for alfalfa, cantaloupe, corn, and wheat

Fig. 4. Box-and-whisker plots of the observed data and the dataproduced by OK, RK, and CK models for alfalfa, cantaloupe, corn,and wheat

when using the OK, RK, and CK models. One plot contains the

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outliers �Fig. 4�a�� and the other does not �Fig. 4�b�� in order tomake the comparison of the performance of the models easier.Box-and-whiskers plots can provide the following quantitativeinformation: �1� the degree of dispersion or spread which is thespacing between the different parts of the box-and-whiskers; �2�the skewness which is the nonequidistance of the median linefrom the middle of the box; �3� the middle 50% of the data, whichis contained inside the box; �4� the 75th and 25th percentile of thedata sets which are the upper and lower edges of the box, respec-tively; �5� the minimum and maximum data values which are theends of the vertical lines or the “whiskers;” �6� the confidenceinterval about the median which is represented by the notches;and �7� the outliers or suspected outliers which are at the ends ofthe whiskers.

From Fig. 4�b� it can be observed that:• The degree of dispersion was overestimated when using the

OK model for alfalfa, corn, and wheat and not for cantaloupe.RK was able to maintain the dispersion for alfalfa, cantaloupe,and wheat and underestimate it for corn. CK maintained thedispersion for cantaloupe, underestimate it for alfalfa and corn,and overestimate it for wheat;

• The skewness was successfully maintained when using thethree models for all crops;

• The middle 50% of the data as well as the 75th and 25thpercentiles were maintained when using OK for cantaloupeand corn, overestimated for alfalfa, and underestimated forwheat. RK was able to maintain them for all crops while CKmaintained them for alfalfa, cantaloupe, and corn, and under-estimated them for wheat;

• The maximum data value was overestimated when using OKfor alfalfa and corn and maintained for cantaloupe and wheatwhile the minimum data value was underestimated for alfalfa,corn, and wheat and maintained for cantaloupe. The maximumdata value was maintained when using RK for all crops whilethe minimum value was maintained for alfalfa, cantaloupe,and wheat and overestimated for corn. The maximum datavalue was underestimated when using CK for alfalfa, canta-loupe, and corn and overestimated for wheat while the mini-mum data value was underestimated for alfalfa, cantaloupe,and wheat and overestimated for corn;

• The confidence interval about the median was maintained bythe three models; and

• The outliers were overestimated when using the three modelswith all crops.Fig. 5 shows examples of the generated soil salinity surfaces

for alfalfa, cantaloupe, corn, and wheat fields using the OK, RK,and CK models. The observed soil salinity points are displayedwith all the generated surfaces as a reference, the closer the sur-face is to the observed points, the better the performance of thatmodel. The OK and RK models were able to capture the smallvariations in the data, and their generated soil salinity surfaces arecloser to the observed points than the CK model soil salinitysurface. The generated soil salinity surfaces using the CK modelperformed as a trend surface model which is clear with the alfalfaand wheat �Fig. 3� and did not capture the small variations in soilsalinity.

Fig. 6 shows bar charts of the NMAE, NRMSE, and G valuesfor alfalfa, cantaloupe, corn, and wheat fields using the OK, RK,and CK models. For most fields the NMAE and NRMSE valuesof the OK model are the smallest and the corresponding valuesfor the CK model are the highest. While the G values for the OKmodel are the highest and the G values of the CK model are the

0.136:355-364.

following: �1� OK; �2� RK; and �3� CK. Based on the modelsresults, the performance of the different crops was evaluatedusing the OK model. From Fig. 6 it can observed that the cornfields have the smallest NMAE and NRMSE values, while thealfalfa fields have the highest NMAE and NRMSE values. Inaddition, the G values of the corn fields are closest to 1 while thecorresponding G values of the alfalfa fields are the farthest from1. Based on these results, the performance of estimates of soilsalinity for different crops is the following: �1� corn; �2� wheat;�3� cantaloupe; and �4� alfalfa.

Conclusions

This study shows that LANDSAT satellite images can be used for

Fig. 5. Examples of generated surfaces for alfalfa, cantalo

improving the mapping of soil salinity. The best band combina-

tions for estimating soil salinity with different crops are as fol-lows: alfalfa �red, near infrared, and NDVI�; cantaloupe �blue andgreen�; corn �near, thermal, and NDVI�; and wheat �blue andthermal�. The OK model performed the best, the RK model per-formed second best, and the CK model had the worst perfor-mance. The better performance of OK over RK may be attributedto the fact that autocorrelation among soil salinity data are higherthan cross correlation between soil salinity and the LANDSATbands. The better performance of RK over CK may be attributedto the fact that in RK adding the residuals to the OLS surfacecaptures the small variations in soil salinity. The crop perfor-mance for estimating soil salinity is the following: �1� corn; �2�wheat; �3� cantaloupe; and �4� alfalfa. The low performance ofalfalfa may in part be attributed to the multiple cuts of alfalfa

orn, and wheat fields using the OK, RK, and CK models

during the growing season which means that the alfalfa biomass

/ JUNE 2010

0.136:355-364.

can change significantly depending on the harvest dates and sat-ellite image acquisition dates.

References

Agterberg, F. P. �1984�. “Trend surface analysis.” Spatial statistics andmodels, G. L. Gaile and C. J. Willmott, eds., Reidel, Dordrecht, TheNetherlands, 147–171.

Akaike, H. �1977�. “On entropy maximization principle.” Applications ofstatistics, P. R. Krishnaiah, ed., North-Holland, Amsterdam, 27–41.

Brockwell, P. J., and Davis, R. A. �1991�. Time series: Theory and meth-ods, Springer, New York.

Douaik, A., Van Meirvenne, M., and Toth, T. �2003�. “Spatio-temporalkriging of soil salinity rescaled from bulk soil electrical conductivity.”Proc., Quantitative Geology and Geostatistics, GeoEnv IV: 4th Euro-pean Conf. on Geostatistics for Enironmental Applications, X.Sanchez-Vila, J. Carrera, and J. Gomez-Hernandez, eds., Kluwer Aca-demic, The Netherlands, 413–424.

Dwivedi, R. S., and Rao, B. R. M. �1992�. “The selection of the bestpossible LANDSAT TM band combination for delineating salt-affected soils.” Int. J. Remote Sens., 13�11�, 2051–2058.

Eldeiry, A., and Garcia, L. A. �2008a�. “Detecting soil salinity in alfalfafields using spatial modeling and remote sensing.” Soil Sci. Soc. Am.

Fig. 6. NMAE, NRMSE, and G values for alfalfa, corn, cantaloupe,and wheat fields using the OK, RK, and CK models

J., 72�1�, 201–211.

JOURNAL OF IRRIG

Eldeiry, A., and Garcia, L. A. �2008b�. Spatial modeling of soil salinityusing remote sensing, GIS, and field data, VDM Verlag, Saarbruken,Germany.

Eldeiry, A., Garcia, L. A., and Reich, R. M. �2008�. “Soil salinity sam-pling strategy using spatial modeling techniques, remote sensing, andfield data.” J. Irrig. Drain. Eng., 134�6�, 768–777.

ERDAS Imagine. �2006�. ERDAS Inc., Leica Geosystems, Atlanta.Farifteh, J., Farshad, A., and George, R. J. �2006�. “Assessing salt af-

fected soils using remote sensing, solute modeling, and geophysics.”Geoderma, 130, 191–206.

Fernández-Buces, N., Siebe, C., Cram, S., and Palacio, J. L. �2006�.“Mapping soil salinity using a combined spectral response index forbare soil and vegetation: A case study in the former Lake Texcoco,Mexico.” J. Arid Environ., 65�4�, 644–667.

Gates, T. K., Burkhalter, J. P., Labadie, J. W., Valliant, J. C., and Broner,I. �2002�. “Monitoring and modeling flow and salt transport in asalinity-threatened irrigated valley.” J. Irrig. Drain. Eng., 128�2�, 87–99.

Gates, T. K., Garcia, J. C., and Labadie, J. W. �2006�. “Toward optimalwater management in Colorado’s Lower Arkansas River Valley:Monitoring and modeling to enhance agriculture and environment.”Completion Rep. No. 205, Colorado Water Resources Research Insti-tute, Fort Collins, Colo.

Goovaerts, P. �1997�. Geostatistics for natural resource evaluation, Ox-ford University Press, New York.

Greenway, H., and Munns, R. �1980�. “Mechanisms of salt tolerance innonhalophytes.” Annu. Rev. Plant Physiol., 31, 149–190.

Guisan, A., and Zimmermann, N. E. �2000�. “Predictive habitat distribu-tion models in ecology.” Ecol. Modell., 135�2–3�, 147–186.

Gumpertz, M. L., Graham, J. M., and Ristaino, J. B. �1997�. “Autologisticmodel of spatial pattern of Phytophthora epidemic in bell pepper:Effects of soil variables on disease presence.” J. Agric. Biol. Environ.Stat., 2�2�, 131–156.

Haining, R. �1990�. Spatial data analysis in the social and environmentalsciences, Cambridge University Press, Cambridge, England.

Howari, F. M. �2003�. “The use of remote sensing data to extract infor-mation from agricultural land with emphasis on soil salinity.” Austral.J. Soil Res., 41�7�, 1243–1253.

Isaaks, H. E., and Srivastava, R. M. �1989�. An introduction to appliedgeostatistics, Oxford University Press, New York.

Istok, J. D., Smyth, J. D., and Flint, A. L. �1993�. “Multivariate geostatis-tical analysis of ground-water contaminant: A case history.” GroundWater, 31, 63–74.

Journel, A. G. �1984�. “mAD and conditional estimators.” Geostatisticsfor natural resources characterization, Part 1, G. Verly et al., eds.,Dordrecht, Boston, D. Reidel Pub. Co., Hingham, Mass.

Journel, A. G., and Huijbregts, C. J. �1978�. Mining geostatistics, Aca-demic Press, New York.

Kravchenko, A., and Bullock, D. G. �1999�. “A comparative study ofinterpolation methods for mapping soil properties.” Agron. J., 91,393–400.

Legendre, P. �1993�. “Spatial autocorrelation: trouble or new paradigm?”Ecology, 74�6�, 1659–1673.

Li, B., and Yeh, T. C. J. �1999�. “Cokriging estimation of the conductivityfield under variably saturated flow conditions.” Water Resour. Res.,35�12�, 3663–3674.

Lichstein, J. W., Simons, T. R., and Franzreb, K. E. �2002�. “Landscapeeffects on breeding songbird abundance in managed forests.” Ecol.Appl., 12�3�, 836–857.

Martinez-Cob, C. A. �1996�. “Multivariate geostatistical analysis ofevapotranspiration and precipitation in mountainous terrain.” J. Hy-drol., 174, 19–35.

Miles, D. L. �1977�. “Salinity in the Arkansas Valley of Colorado.” In-teragency Agreement Rep. No. EPA-IAG-D4-0544, EPA, Denver.

Miller, J., Franklin, J., and Aspinall, R. �2007�. “Incorporating spatialdependence in predictive vegetation models.” Ecol. Modell., 202�3–4�, 225–242.

Odeh, I. O. A., McBratney, A. B., and Chittleborough, D. J. �1995�.

0.136:355-364.

“Further results on prediction of soil properties from terrain attributes:Heterotopic cokriging and regression-kriging.” Geoderma, 67�3–4�,215–226.

Phillips, J. D. �1986�. “Measuring complexity of environmental gradi-ents.” Vegetatio, 64, 95–102.

Ripley, B. D. �1981�. Spatial statistics, Wiley, New York.Robbins, C. W., and Wiegand, C. L. �1990�. “Field and laboratory mea-

surements.” Agric. salinity assess. and manage, K. K. Tanji, ed.,ASCE, Reston, Va., 203–219.

Robertson, G. P. �1987�. “Geostatistics in ecology: Interpolating withknown variance.” Ecology, 68�3�, 744–748.

Schloeder, C. A., Zimmermann, N. E., and Jacobs, M. J. �2001�. “Com-parison of methods for interpolating soil properties using limiteddata.” Soil Sci. Soc. Am. J., 65, 470–479.

Shouse, P. J., Gerik, T. J., Russell, W. B., and Cassel, D. K. �1990�.“Spatial distribution of soil particle size and aggregate stability indexin a clay soil.” Soil Sci., 149, 351–360.

Song, C., Woodcock, C. E., Seto, K. C., Lenney, M. P., and Macomber, S.A. �2001�. “Classification and change detection using LANDSAT TMdata: When and how to correct atmospheric effects?” Remote Sens.Environ., 75, 230–244.

Stein, A., and Corsten, L. C. A. �1991�. “Universal kriging and cokrigingas a regression procedure.” Biometrics, 47, 575–588.

Stein, A., van Dooremolen, W., Bouma, J., and Bregt, A. K. �1988�.“Cokriging point data on moisture deficit.” Soil Sci. Soc. Am. J., 52,1418–1423.

Tanji, K. K. �1990�. Agricultural salinity assessment and management,ASCE, Reston, Va.

Trangmar, B. B., Yost, R. S., Wade, M. K., Uehara, G., and Sudjadi, M.�1987�. “Spatial variation of soil properties and rice yield on recentlycleared land.” Soil Sci. Soc. Am. J., 51, 668–674.

Triantafilis, J., Odeh, I. O. A., and McBratney, A. B. �2001�. “Five geo-statistical models to predict soil salinity from electromagnetic induc-tion data across irrigated cotton.” Soil Sci. Soc. Am. J., 65�3�, 869–878.

Vauclin, M., Vieira, S. R., Vachaud, G., and Nielsen, D. R. �1983�. “Theuse of cokriging with limited field observations.” Soil Sci. Soc. Am. J.,47, 175–184.

Yates, S. R., and Warrick, A. W. �1987�. “Estimating soil water contentusing cokriging.” Soil Sci. Soc. Am. J., 51, 23–30.

Zhang, R., Myers, D. E., and Warrick, A. W. �1992�. “Estimation of thespatial distribution of the soil chemicals using pseudo cross-variograms.” Soil Sci. Soc. Am. J., 56, 1444–1452.

Zhang, R., Shouse, P., and Yates, S. �1997�. “Use of pseudo-crossvariograms and cokriging to improve estimates of soil soluteconcentrations.” Soil Sci. Soc. Am. J., 61, 1342–1347.

/ JUNE 2010

0.136:355-364.

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